Transformation of Nonlinear Systems into State Affine Control Systems and Observer Synthesis

Abstract This paper addresses the synthesis of observers for nonlinear systems and their equivalence to state affine systems (i.e. time-varying linear systems). Necessary and sufficient conditions are given and then, whether a solution exists, one gets the observer synthesis. These constructive conditions are based on the analysis of thesystem input/output (I/O) differential equation. The transformed system is again transformed to solved an algebraic Ricatti 's equation instead of a time varying one.